Q8 of 37 Page 14

In the following data, find the values of p and q. Also, find the median class and modal class. [CBSE 2013]


Class

Frequency (f)

cummulative frequency (cf)

100 - 200

11

11

200 - 300

12

P

300 - 400

10

33

400 - 500

Q

46

500 - 600

20

66

600 - 700

14

80

To find p and q, solve by finding cumulative frequency,


CLASS

FREQUENCY (f)

CUMULATIVE FREQUENCY (Cf)

100 - 200

11

11

200 - 300

12

p = 11 + 12 = 23

300 - 400

10

33

400 - 500

q

46 = 33 + q ⇒ q = 13

500 - 600

20

66

600 - 700

14

80

⇒ p = 11 + 12 = 23


And 46 = 33 + q ⇒ q = 46 – 33 = 13


∴ p = 23 and q = 13


Lets form the table again,



CLASS

FREQUENCY (fi)

CUMULATIVE FREQUENCY (Cf)

100 - 200

11

11

200 - 300

12

23

300 - 400

10

33

400 - 500

13

46

500 - 600

20

66

600 - 700

14

80

TOTAL

80

  

For modal class,


Here, the maximum class frequency is 20.


The class corresponding to this frequency is the modal class. ⇒ modal class = 500 - 600


To find median class,


Assume Σfi = N = Sum of frequencies,


fi = frequency


and Cf = cumulative frequency


So, N = 80


⇒ N/2 = 80/2 = 40


The cumulative frequency just greater than (N/2 = ) 40 is 46, so the corresponding median class is 400 - 500.


∴ modal class = 500 - 600 and median class = 400 - 500

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